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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.util.FastMath;
/**
* This class implements the 5(4) Higham and Hall integrator for
* Ordinary Differential Equations.
*
* <p>This integrator is an embedded Runge-Kutta integrator
* of order 5(4) used in local extrapolation mode (i.e. the solution
* is computed using the high order formula) with stepsize control
* (and automatic step initialization) and continuous output. This
* method uses 7 functions evaluations per step.</p>
*
* @since 1.2
*/
public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
/** Integrator method name. */
private static final String METHOD_NAME = "Higham-Hall 5(4)";
/** Time steps Butcher array. */
private static final double[] STATIC_C = {
2.0/9.0, 1.0/3.0, 1.0/2.0, 3.0/5.0, 1.0, 1.0
};
/** Internal weights Butcher array. */
private static final double[][] STATIC_A = {
{2.0/9.0},
{1.0/12.0, 1.0/4.0},
{1.0/8.0, 0.0, 3.0/8.0},
{91.0/500.0, -27.0/100.0, 78.0/125.0, 8.0/125.0},
{-11.0/20.0, 27.0/20.0, 12.0/5.0, -36.0/5.0, 5.0},
{1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0}
};
/** Propagation weights Butcher array. */
private static final double[] STATIC_B = {
1.0/12.0, 0.0, 27.0/32.0, -4.0/3.0, 125.0/96.0, 5.0/48.0, 0.0
};
/** Error weights Butcher array. */
private static final double[] STATIC_E = {
-1.0/20.0, 0.0, 81.0/160.0, -6.0/5.0, 25.0/32.0, 1.0/16.0, -1.0/10.0
};
/** Simple constructor.
* Build a fifth order Higham and Hall integrator with the given step bounds
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param scalAbsoluteTolerance allowed absolute error
* @param scalRelativeTolerance allowed relative error
*/
public HighamHall54Integrator(final double minStep, final double maxStep,
final double scalAbsoluteTolerance,
final double scalRelativeTolerance) {
super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
}
/** Simple constructor.
* Build a fifth order Higham and Hall integrator with the given step bounds
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param vecAbsoluteTolerance allowed absolute error
* @param vecRelativeTolerance allowed relative error
*/
public HighamHall54Integrator(final double minStep, final double maxStep,
final double[] vecAbsoluteTolerance,
final double[] vecRelativeTolerance) {
super(METHOD_NAME, false, STATIC_C, STATIC_A, STATIC_B, new HighamHall54StepInterpolator(),
minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
}
/** {@inheritDoc} */
@Override
public int getOrder() {
return 5;
}
/** {@inheritDoc} */
@Override
protected double estimateError(final double[][] yDotK,
final double[] y0, final double[] y1,
final double h) {
double error = 0;
for (int j = 0; j < mainSetDimension; ++j) {
double errSum = STATIC_E[0] * yDotK[0][j];
for (int l = 1; l < STATIC_E.length; ++l) {
errSum += STATIC_E[l] * yDotK[l][j];
}
final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));
final double tol = (vecAbsoluteTolerance == null) ?
(scalAbsoluteTolerance + scalRelativeTolerance * yScale) :
(vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);
final double ratio = h * errSum / tol;
error += ratio * ratio;
}
return FastMath.sqrt(error / mainSetDimension);
}
}
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